## Journal of Applied Mathematics

### Quenching Time Optimal Control for Some Ordinary Differential Equations

Ping Lin

#### Abstract

This paper concerns time optimal control problems of three different ordinary differential equations in ${\Bbb R}^{2}$. Corresponding to certain initial data and controls, the solutions of the systems quench at finite time. The goal to control the systems is to minimize the quenching time. The purpose of this study is to obtain the existence and the Pontryagin maximum principle of optimal controls. The methods used in this paper adapt to more general and complex ordinary differential control systems with quenching property. We also wish that our results could be extended to the same issue for parabolic equations.

#### Article information

Source
J. Appl. Math., Volume 2014 (2014), Article ID 127809, 13 pages.

Dates
First available in Project Euclid: 2 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.jam/1425305676

Digital Object Identifier
doi:10.1155/2014/127809

Mathematical Reviews number (MathSciNet)
MR3198357

#### Citation

Lin, Ping. Quenching Time Optimal Control for Some Ordinary Differential Equations. J. Appl. Math. 2014 (2014), Article ID 127809, 13 pages. doi:10.1155/2014/127809. https://projecteuclid.org/euclid.jam/1425305676

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